Question: Solve for $x$ and $y$ using substitution. ${-6x+5y = -9}$ ${x = 5y-11}$
Answer: Since $x$ has already been solved for, substitute $5y-11$ for $x$ in the first equation. ${-6}{(5y-11)}{+ 5y = -9}$ Simplify and solve for $y$ $-30y+66 + 5y = -9$ $-25y+66 = -9$ $-25y+66{-66} = -9{-66}$ $-25y = -75$ $\dfrac{-25y}{{-25}} = \dfrac{-75}{{-25}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x = 5y-11}\thinspace$ to find $x$ ${x = 5}{(3)}{ - 11}$ $x = 15 - 11$ ${x = 4}$ You can also plug ${y = 3}$ into $\thinspace {-6x+5y = -9}\thinspace$ and get the same answer for $x$ : ${-6x + 5}{(3)}{= -9}$ ${x = 4}$